Applying Decision Science and

Game Theory to Suicidal Behaviors

Decision-Making Models of Functional Psychopathology

Lawrence Amsel, MD, MPH Director of Dissemination Research for

Trauma Studies and Services

Collaborators / Co-authorsAvital Pilpel

Randall Marshall

Applying Decision Science to Clinical Psychiatry

• Examples of application of models and concepts from decision science to clinical psychiatry

• Modeling Ambivalent Suicide Attempts • Effecting Change in Clinicians Behavior• Modeling Addictions with Discounting• Deconstructing “Impulsivity”• Decision Deficits in OCD• Decision Deficits in Pathological Gambling• Social Phobia and Ultimatum Game• Conjectures on the Nature of the Anxiety-Avoidance

Relationship

Outline of Talk II Introduction: Suicidal Behaviors, Ideation and

DecisionsII Mathematical Modeling, Translational Research, and

Transdisciplinary Research – Comparing animal models to mathematical models– Why Decision Science should care about suicide ( and other

aspects of psychopathology). – Why Psychiatrists should care about Decision Science

III The Research Agenda of the Neurobiology of SuicideIV Towards a decisional (formal) model of suicidal

behaviorsA. Mixed Strategy Model of Suicide BehaviorB. Adding Inter-temporal Choice and Future Discounting – a Markov

ModelC. Signaling Game Model – Modeling the Relationship Aspects of

Some Suicidal Behaviors

Outline of Talk IIV Lessons from Suicide Modeling

•  Theoretical Framework for suicidology• Alternative frame for analyzing existing data • Source of alternative operationalizations of key concepts and risk

factors in suicidology and Other aspects of Psychological Dysfunction

VII Taking Decision Making and Decision Science Seriously

VII Future Directions – With Peter Jensen – Applying Decision Science to Dissemination of

guidelines– With Randall Marshall – Applying Decision Science to

Dissemination of CBT for PTSD Personal Journey– With Robert Rogers, Randall Marshall, Frank Schneier, Blair

Simpson – Risk Perception and Decision Tasks in Anxiety Disorders

Suicidal Behviors• Completed Suicide: Rates about 3/100,000/ Year in US =

30,000/Year• Suicide Attempt 10-100 times more common than

Completed – The ER Nightmare –Major Source of Mortality in Psychiatric Practice

• Suicidal Preparation (Hoarding Pills): Rates Unknown • Suicidal Intent w/o Preparation: Rates Unknown• Suicidal Ideation – Quite Common, some estimates are

20% of young adults• The vast majority of suicides have seen a clinician within

the months preceding the suicide• Yet, despite extensive research programs, predicting

suicidal behavior has been an elusive goal

Risk Factors for Suicide I• Suicidal Thoughts and Behaviors

– Suicidal Ideas, Plans, Attempts (current or past)– Suicidal Intent– Lethality of Plans or Attempt

• Psychiatric Diagnosis• Physical Illness• Psychosocial features

– Loss of Social Support– Unemployment ( Recent Loss of Job)– Drop in Socioeconomic Status– Poor Family Ties– Domestic Violence– Other Life Stressors

Risk Factors for Suicide II• Childhood Trauma

– Sexual or Physical or Psychological Abuse

• Genetic Familial Factors– Family History of Suicide ( see Hemingways) – Family History of Mental Illness

• Psychological Features– Hopelessness– Psychic Pain– Severe Anxiety– Panic Attacks– Shame or Humiliation– Psychological Turmoil– Loss of Self Esteem– Narcissistic Vulnerability– Agitation – Impulsivity – Aggression

Risk Factors for Suicide III• Cognitive Features

– Executive Function Impairments– Thought Constriction ( Tunnel Vision)– Polarized Thinking Style– Closed Mindedness

• Demographic Features– Male Gender ( But see New York City Police) – Widowed, Divorced or Single ( Especially for men)– Adolescents are group with highest number of suicides (Third Leading Cause of Death

In 15-19 Year-olds, After Accidents and Homicides., 7.4 /1000,000/Yr, = 1,500 Deaths per year in US

– White Race ( BUT See Police) – Gay, Lesbian, or Bisexual Orientation

• Other Features– Access to Firearms– Intoxication– Substance Abuse

• Protective Features– Children in Home or Responsibility to Family ( Except for Post Partum MDD)– Pregnancy ( Except post-partum depression/psychosis)– Religiosity– Life Satisfaction– Reality Testing– Positive Coping Skills / Problem Solving Ability– Social Support– Therapeutic Relationship / SOMATIC ANXIETY

The Prediction Problem - I

Non SuicideIdeator

SuicideIdeator

Low Lethality Attempter

High LethalityAttempter

Suicide Completer

p1

p10

p1

p2

p1

p1

p1

p1

p1

p8p

9

p6

p5

p7

p4

p3

The Prediction Problem -II

• Clinicians deal with ideators and attempters and need to predict probability of transition to attempter status or completer status in future.

• Only a small fraction of ideators actually make an attempt. P2 <<< 1 and P9 <<< 1. Only a fraction of attempters complete suicide. P7 < 1 and P4 << 1.

• Perhaps only high-lethality attempters are at high risk for completion – accidents excepted.

• The risk relationships between these behaviors is not that clear BECAUSE THERE IS NO BEHVIORAL THEORY TO GUIDE RESEARCH

Translational Research and Mathematical Modeling

Translational Research and Mathematical Modeling Analogous

Animal Behavior Human Behavior

Empirical (Evolutionary Preservation) Study

Isomorphic? Basic Mechanism Human Mechanism (Dopamine Cell Function) (Dopamine Cell Function?) Mathematical Model ? Human Behavior

Logical (Rationality Assumption? ) Deduction

Complex Mechanism ? Human Mechanism (Game Theory Solution Set)

Why Psychiatric Suicidologists Should Care

to Study Rational Choice Models

• Decision making requires integrating basic capacities into an organized cognition/behavior – a decision (recall your mental experiences in the ultimatum game)

• Yet decision making appears to be below the complexity level of clinical phenomena and thus a potential explanation for them e.g. a deficit in discounting may underlie addictive behaviors

• Decision-making is at a complexity level between clinical phenomenon and basic neuro-bio-psychological functional modules.

Why Psychiatric Suicidologists Should Care

to Study Rational Choice Models

• Because of its unique place in the hierarchy of behavioral complexity – more complex that most basic neuropsych functionalities we usually measure but less complex than clinical symptoms- decision making involves interactions of simpler systems , anatomical, neurochemical, and psychological

• As the following talks will show decision making concepts appear to map nicely onto the interaction of these anatomical, pharmacological as well as cognitive structures allowing for experimental work in imaging, pharmacologic manipulation of behavior, and contextual manipulation of cognitive processes

• In other words its good way to use our currently available research toys… tools.

Why Psychiatric Suicidologists Should Care

to Study Rational Choice Models • The work of Kahneman and Tversky on judgment and decision

anomalies (among normals) was only possible once a highly developed normative theory was in place against which to test human behavior

• Similarly with emotional components of decision making which are now being incorporated into decision science.

• These aren’t failures but serial successes of the research program• It is also important to note that rational choice axioms don’t

preclude seemingly irrational behavior once there are two people involved as in the Prisoners Dilemma.

• Rational choice need not lead to intuitively ‘sensible’ behaviors- In humans even the (axiomatically) rational s irrational

Why Decision Science Should Study

Suicide and its Models • Important Public Health Problem in Its Own Right• End of Life Decisions – Health Care policy

– Healthcare doesn’t work in America• Costs of Cars’ steel vs. Healthcare and outsourcing

• End of Life Costs a Major Factor

• End of Life Decisions – Bioethics– Wedge Issue Similar to Abortion

– Life Boundary Issues – Beginning, End, Ownership and Right

Why Decision Science Should Care to Study

Suicide and Its Modeling • Rational Choice Modeling of Suicide and Related

Questions of Determining a Utility Function for Life Itself

• One’s most Valued Commodity • Greatest Liability• Capital Asset

– Production Function

• Individual Marketplace• Integrated Discounted Consumption Basket• Meaning/Signal Based Value Assessment

– Contextual Specific Signal / Values / License– Moral High ground– License to Kill

Why Decision Science Should Care to

Study Suicide and Its Modeling – The Dynamics of Spending or Risking Life in

Political Marketplace– Almost Never see this in Economic

Marketplace Exception: Life insurance, Suicide

– When does one spend Life, or appear to, and what does it buy (Castro in the Mountains)

– Willingness to die as a license to kill

Why Decision Scientists Should Care to

Study Suicide and its Models • Meaning / Signal Based / Licensing and Value

Assessment• Contextually Specific Values• Moral Currency Not Quite the High ground• Is a Uniform a License to Kill • Is willingness to die without uniform a license to kill

– Uniformed vs. Clandestine ( when is uniform advantageous) – Target Civilian vs. Combatant vs. Both – Risky Missions vs Suicide ( do S justify lack of uniform /civilian target?)

» Symmetric Information vs. Asymmetric » Relate to Notion of Asymmetric War and Asssymetry of material

forces » For Whom is The Signal ( Signals) Intended

– Communal Induction of Strategic Emotion– Community as Suicides antitheses reversal for suicide bombers

Research Agenda for Neurobiology of Suicidal Behaviors

Biological Factors Neuro-chemical

AnatomicalEtc

Basic Modular Neuropsychological Functions

Suicidal Behaviors

Operationalized (Psychometric)

Behavior and cognitions related to suicidal risk

Beck Depression Scale Impulsivity Scale

Hopelessness Scaleetc.

Role of Decision Science for Neurobiology of Suicidal Behaviors

Biological Factors Neuro-chemical

AnatomicalEtc

Basic Neuropsychological Functions

Suicidal Behaviors

Behavior and cognitions related

to suicidal risk

Beck depressionImpulsivity

Hopelessness etc.

Rational Choice Models

“neuro-economics”

Expanded Stress Diathesis Model: Incorporating a Decisional Axis

Non-Decisional Factors

“Motivation”

(Judgment”)

Decision Deficits

DiathesisTrait

Chronic

Beck Depression

Hopelessness

(Beck- Hamilton Gap)

Aggression

Impulsivity

Hx Head Injury

StressState

Acute

Hamilton

Life Events

Psychosis

Intoxication

Manic irritability

HPA –NE effects

What Decision Science has to Offer:Decision Modeling

• Formal Modeling offers a framework for conceptualizing an area of behavior as well as a ‘normative” model, both of which generate empirically testable questions: Rational Choice Models have made the Study of Bias, Heuristics, and Emotions Possible

• Formal Modeling suggests alternative operational-ization of key cognitive concepts and behavioral tendencies

• Formal Modeling offers alternative approaches to analyzing existing data

Decision Theory Modeling

• This study aimed at developing models based on Game Theory that would incorporate what is known about suicidal risks and behaviors

• Explanatory• Unifying • Predictive• Hypothesis Generating

“Economic” Modeling of Suicide

• The real definition of originality• Darwinian model (deCatanzaro, 1986)• Cost-Benefit analysis (Yeh et al, 1987)• Demand Supply model (Yang et al, 1996)• Labor Force model (opportunity set?) (Huang, 1991)• Investment under uncertainty (Dixit et al, 1994)• Game theory model – suicide as signaling behaviors

(Rosenthal, 1993)• Strategic Suicide (Norberg et al, 2000)

Naïve Expected Utility Model

U (Status quo)

U (Death)

Decision

Where U(X ) = The subjective Utility of a state

Mixed Strategies Model• Nash equilibrium based on need for Mixed Decision

Strategies• The idea of mixed strategies is that sometimes the

only good response to uncertainty is even more uncertainty, deliberate uncertainty.

• Examples Menu Coalitions, Balanced portfolio, Coin toss

• Key insight: The real decision is whether to make an attempt. This is a decision under uncertainty.

Mixed Strategy Model

Attempt

U(Status Quo)

U(New Status)

U(Death)

p(Death) ~ f (Attempt lethality,

and /or Intent)

Decision

No Attempt

Mixed Equilibrium Model• The “solution” is a mixed strategy in which dying

and surviving are both seen as possible outcomes with varying probabilities.

• In formal terms this is high stakes lottery. • FORMAL MODEL OF AMBIVALENCE• The decision maker (DM) chooses an attempt with a

particular probability parameter – namely the lethality of the attempt.

• “Nature-Chance” then dictates the actual outcome --state of affairs.

• For now we assume that the utilities are independent of the probability.

Mixed Equilibrium Model

Attempt

U(Status Quo)

U(New Status)

U(Death)

p(Death) ~ f (attempt lethality)

Decision

No Attempt

Mixed Equilibrium Model

• The utility of not attempting suicide is U(SQ). • The Expected Utility (EU) of attempting suicide

with lethality p is weighted average of surviving and dying EU = pU(d)+(1-p)U(NS)

• The DM will attempt suicide whenthe probability of Death p0 is such that

U(SQ) < p0U(D)+(1-p0)U(NS)

• The question is, when will that be the case?

Implications of the Model I

• While the naïve model allows for only two cases

• U(D) < U(SQ) or U(SQ) < U(D)

• The current model implies six cases

• Three for U(D) < U(SQ) – “No Death Wish”

– U(D) < U(NS) < U(SQ) -- Normal -- Not an attempter

– U(NS) < U(D) < U(SQ) -- Samurai -- Not an attempter

– U(D) < U(SQ) < U(NS) -- “manipulative” -- Only low lethality

Implications of the Model II

• Three for U(SQ) < U(D) - “Death Wish”• U(SQ) < U(D) < U(NS) -- Desperation -- Prefers Low

lethal

• U(NS) < U(SQ) < U(D) --Cautious Terminal -Only high lethal

• U(SQ) < U(NS) < U(D) --Hopeless --Prefers high lethal

Implications of the Model III• Consider U(D) < U(SQ) < U(NS): --“the

manipulative gesture”

• The indifference point p0 is given by: p0= [U(NS) - U(SQ)] / [U(NS)- U(D)]

• [U(NS) - U(SQ)] is the potential utility gained from surviving an attempt. Call this the Gain, which is a positive quantity

• [U(NS)- U(D)] = {[U(NS) – U(SQ)] + [U(SQ) – U(D)]}

• [U(SQ) – U(D)] is the current perceived Value of Living (VoL) which is positive.

Implications of the Model IV

• Thus to “take the gamble” •

p0 <= Gain______ Gain + VoL

• The quantity above depends on the relative perceived worth of Gains compared to current VoL.

• In general this DM makes only low lethality attempts.

• But depression (decrease in VoL) or neediness (increase in Gains) will increase acceptable lethality .

Implications of the Model V

• The difference U(SQ) – U(D) is not by itself predictive of attempt. The literature bears this out as severity of depression does not correlate well with attempter status

• Risk of an attempt depends on U(NS) a factor rarely elicited in suicide risk assessment

• The lethality level chosen depends on U(NS). The model predicts that the availability of a method ( of a particular lethal potential) is extremely important in determining if an attempt occurs, as borne out in the literature.

• FORMAL MODEL OF LETHALTY INTENT LEVEL• Thus, prevention strategy is type dependant -- e.g.

removing firearms -- may not help for the wrong type

Implications of the Model VI• This DM prefers status quo to death but is willing

to risk death at some level to arrive at a desired post attempt state. (like Army volunteers). This could be a change in status in family relations in financial or legal situation it could be a desired hospitalization.

• In this case the attempt will be limited to low lethality methods, as is found in certain adolescents who make dramatic but low lethal attempts in order to influence a situation about which they feel they are helpless to change in any other way.

Implications of the Model VII

• Risk assessment is often done on basis of estimates of patients wish to die instead of their willingness to make an attempt.

• Yet this model indicates that some of the truly suicidal will not make an attempt unless the correct lethality level is available.

• Similarly, some non-suicidal will make an attempt under right conditions.

Implications of the Model VIIIModel predicts that one could reduce risk in

“manipulative” type by reducing U(NS) this is

consistent with Kernberg's contracting of the

therapeutic frame in which specific disincentives

are part of the therapy for this specific patient type.

This may be the basis for clinical practice of

“contracting for safety” with suicidal patients

Markov Model• This previous model assumes that the Status

Quo is permanent.

• A more realistic model must include the fact that patients status changes, and they have some expectation of the possibility of this change—

• Hope and its opposite Hopelessness

The Markov Model

DepressedState

RecoveryP(s)

P(r)

P(w)

P(t)

The Markov Model

Depressed Recovered

Depressed P(s)

0.8

P(r)

0.2

Recovered P(w)

0.1

P(t)

0.9

Markov Model

• This introduces three new parameters, the first is p(R) perceived probability of recovery --

• The second is the degree of expected recovery reflected in the Utility of recovery.

• Third is discount rate on future well being• Taken together these may correspond to

measurements of hopelessness that strongly correlate with suicidal status …

• FORMAL MODEL OF HOPLESSNESS

Markov Model

Attempt

U(NS)

U(D)

p(D)

{{<<} }n

RecoveryRecovery

NoAttempt SQ

U(R)

p(R)

Markov Model• The third parameter relates to when one

expects to recover.

• How long will it take?

• Can I hold on?

• This introduces a discounting factor which may relate to degree of impulsivity in suicidal behavior – (a well established risk factor).

• FORMAL MODEL OF IMPULSIVITY

Markov Model• Closely related to this is an unexpected

bonus that fell out of this model, namely the protective effect of future potential attempts.

• “Suicidal thoughts have gotten me through some bad nights” Nietzsche

• The only thing that keeps me from attempting suicide is that I could do it tomorrow –and I hold on one day at a time (Patient comment).

• Suicide attempt are “at the margin”.

Signaling Game Model• Question –In the case of a “manipulative’ attempt (we

don’t like this word) doesn’t the DM have to take into account the reaction of others?

• Might That reaction not depend on the nature and lethality of the attempt?

• Signaling games are a class of games that have been studied that precisely model this attempt situation

• As a benefit it help us get rid of the word ‘manipulative’

• Unless you want to grant that all signaling games including dressing well for an interview are also ‘manipulative’.

Signaling Game ModelS ign a ling G am e

M a rko v C h a in

S ta tus Q uo R e co v er

N o A tte m ptS Q

E m p athy A ng er

P La yer 2

S urv ive D on 't S urv ive

A ttem p t Lo w L e tha li ty

D on 't S urv ive

E m p athy A ng er

P layer 2

S urv ive

A ttem pt H ig h L e tha li ty

P layer 1

N atu re C o py o f G a m e T re e fo r a no the r type

Signaling Game ModelL. Amsel, 2001

Recovery

U(D)

U(NS-L)

U(NS-H)pL (D)

U(NS-L)

U(NS-H)

pH (D)

(Nature)

{{<<}

}nRecovery

U(R)

Attempt Low

Attempt High

Status Quo

(copy of above for another type)

Signaling Game Model• As in all signaling games there is asymmetric information.

• The ‘first player’ ie the suicidal patient knows his intentions and thus his real ‘type’ the ‘second’ player e.g. The clinician or family member does not.

• The first player chooses a strategy to signal the second player as to type namely that U(D)> U(SQ).

• There is a cost to this signaling, which is a higher risk of death than the first player intrinsically wants, which is the dangerous part. Thus the lethality level chosen depends not only on the acceptable risk level given the potential outcomes, it also depends on the first player’s belief about the other’s reaction to different lethality levels.

• There may be cultural conventions that prescribe intensive responses at low levels of attempt and are thus protective.

Signaling Game Model• FORMAL MODEL OF MANIPULATION

• Behavior (not verbalization) that signals that an individual belongs to one type when in fact they belong to another type is a model of manipulation and may be the basis of countertransferential anger elicited by certain character pathologies –

• Not playing by the Rules of The Game

Signaling Game Model• Because it’s a signaling game we assume that

U(NSQ-H) > U(NSQ-L)• In the discrete case with only choices of High and

Low lethality this leads to twelve possible types – ( the orderings on four outcomes divided by 2 because U(NSQ-H) > U(NSQ-L))

• These types react in characteristic ways based on preference structures among U(D), U(SQ), U(NS-L), U(NS-H)

• Thus we would need to know these Utilities to predict suicide risk – this needs testing!

Formal (Mathematical) Modeling Forces the Clarification of Psychiatric Concepts

Difference between Concept Modeling and Operationalzing

• Ambivalence – Mixed Nash Equilibrium

• Lethality Intension - probability distribution of above

• Hopelessness – • Probability of recovery

• Estimate of extent of recovery

• Discounting of Recovery

• Attenuated processing of gain or loss cues

• Loss frame mis-contextualization

• Manipulation – Signaling Game Solution

Formal (Mathematical) Modeling Forces the Clarification of Psychiatric Concepts

Difference between Concept Modeling and Operationalzing

• Impulsivity – • Utility ( Reward loss Cues) • Discounting rate -- time to reward• Reduced time to decision• Risk Seeking• Decreased harm avoidance• Poor assessment of risk probabilities• Meta-cognitive deficit – poor “deciding” about how to decide –inappropriate

cognitive tool choice

• Aggressivity• Overconfidence in Judgment • Non-Impulsive High Risk Bias ( In loss frame only?)• Decision-Implementation linkage

• Reasons for Living Scale (Gap with life events)• Subjective Experience of Depression (Gap with Hamilton)

• Attenuated processing of gain or loss cues

Summary I• We Have shown that the Suicide Prediction

problem incorporates a number of Operationalized but not well modeled psychiatric Concepts

• With the aid of decision science we have shown how formal modeling can sharpen these concepts and lead to further empirical testing via operationalzing the model components

Summary II• Decision Theoretic models of suicidal behavior are consistent with

the published phenomenology, and may lead to an improved ability to predict and prevent suicidal behaviors.

• Decision theoretic models may help explain certain suicidal behaviors that appear anomalous as well as generating testable hypothesis about these behaviors

• Thus suicidal behaviors might best understood by using Normative Decisional perspective as well as incorporating deviations from this, as in theories of Bounded Rationality

• This perspective is part of a larger intellectual convergence within Mathematical Psychology/Psychiatry between Decision Theory and Behaviorism - which are two approaches divided by differing terminologies